Discriminant feature extraction for image recognition using complete robust maximum margin criterion

Maximum margin criterion (MMC) is a promising feature extraction method proposed recently to enhance the well-known linear discriminant analysis. However, due to the maximization of L2-norm-based distances between different classes, the features extracted by MMC are not robust enough in the sense that in the case of multi-class, the faraway class pair may skew the solution from the desired one, thus leading the nearby class pair to overlap. Aiming at addressing this problem to enhance the performance of MMC, in this paper, we present a novel algorithm called complete robust maximum margin criterion (CRMMC) which includes three key components. To deemphasize the impact of faraway class pair, we maximize the L1-norm-based distance between different classes. To eliminate possible correlations between features, we incorporate an orthonormality constraint into CRMMC. To fully exploit discriminant information contained in the whole feature space, we decompose CRMMC into two orthogonal complementary subspaces, from which the discriminant features are extracted. In such a way, CRMMC can iteratively extract features by solving two related constrained optimization problems. To solve the resulting mathematical models, we further develop an effective algorithm by properly combining polarity function and optimal projected gradient method. Extensive experiments on both synthesized and benchmark datasets verify the effectiveness of the proposed method.